Modularity produces small-world networks with dynamical time-scale separation

The Institute of Mathematical Sciences, C.I.T. Campus - Taramani, Chennai, 600 113 India

Corresponding authors: rajkp@imsc.res.in sitabhra@imsc.res.in

Received: 16 December 2008
Accepted: 5 March 2009

Abstract

The functional consequences of local and global dynamics can be very different in natural systems. Many such systems have a network description that exhibits strong local clustering as well as high communication efficiency, often termed as small-world networks (SWN). We show that modular organization in otherwise random networks generically give rise to SWN, with a characteristic time-scale separation between fast intra-modular and slow inter-modular processes. The universality of this dynamical signature, that distinguishes modular networks from earlier models of SWN, is demonstrated by processes as different as spin-ordering, synchronization and diffusion.